There are two types of eccentric motion of a yawed shell. These are nutation and precession. Nutation is a rapid eccentric rotation (the rate of the shell's spin) around the longitudinal axis of the shell. Since it is around the longitudinal axis of the shell and it is eccentric, it prevents the shell from striking nose on in all cases. Precession is a slow eccentric rotation around an off-axis which passes through the shell's center of gravity. Since precession becomes manifest slowly, it requires some distance after yaw is induced before it becomes significant. This is why two plates in direct contact with each other provide less effective thickness than if the plates have space between them. If the distance between the plates is great enough (such as two deck levels rather than one or less) then the combined effects of nutation and precession become more fully manifest providing a greater effective thickness to the armour system.
The axis around which both nutation and precession rotates should not be confused with the path axis of the shell's trajectory. There is usually a trajectory change more toward the normal when a shell passes through heavy armour. In the case of battleship caliber shell passing through the Bismarck class' 50mm upper deck the amount of trajectory change toward the normal is not significant. If I recall correctly the deck would need to be around 7-inches thick for it to provide net
significant trajectory change toward the normal. Nonetheless, studies indicate it is the reduction of kinetic energy that mainly induces yaw, rather than trajectory change.
Although I do feel that the effects of decaping, shell damage and yaw are accumulative.
De-capping provides its own reduction of the shell's penetration potential in several ways. Firstly, it reduces the mass of the shell by around 13%. This in turn reduces the kinetic energy of the shell in addition to the reduction already caused by the energy expended by penetrating the de-capping plate. The cap also helps the shell to penetrate the remaining armour so its loss reduces the penetrative capability of the shell beyond just the reduction of its mass and kinetic energy. German research revealed that if the primary armour had a tensile strength of 80kg/mm2 or higher, it required that a de-capped shell would require more velocity to obtain penetration than the same weight and caliber of shell that was capped. So we indeed see an accumulation of factors that each require more velocity of the shell to obtain penetration, at least off setting the expected reduction of effective thickness by using divided armour thickness-provided the system is designed correctly. The Germans calculated that their spaced array deck armour provided at least the sum thickness of the plates or a little more in terms of effective thickness.
American tests during WW2 of some spaced array systems indicated that yaw could provide as much as a + 30% enhancement of effective thickness in some cases.